simplify, multiply & divide rational expressions
TRANSCRIPT
Simplify, Simplify, Multiply & Multiply &
Divide Rational Divide Rational ExpressionsExpressions
VocabularyVocabulary• Rational Expression Rational Expression - An expression
that can be written as a ratio of 2 polynomials
• Excluded Value Excluded Value – A number that makes a rational expression undefined.
• Simplest form of a rational expression Simplest form of a rational expression – Numerator and denominator have no factors in common other than 1.
How can I How can I simplify?simplify?
EX.EX. Simplify the expression. Simplify the expression. State the excluded value.State the excluded value.
2 2
2 3 3 4
18 303. 4.
6 3
x y z
x x y z
1. Divide Numbers
2. Simplify Variables
EX.EX. Simplify the expression. Simplify the expression. State the excluded value.State the excluded value.
212 6 4( 3)5. 6.
24 6( 3)
x x x
x x
Divide the Divide the PolynomialPolynomial
Multiply Rational Multiply Rational FunctionsFunctions
2 3 2 4 3
2 2 4
14 9 15 217. 8.
3 2 3 5
x x y z x y
x x y yz
1. Multiply Numerators
2. Multiply Denominators
3. Simplify (See previous slide)
Divide Rational Functions “Keep Divide Rational Functions “Keep Change Flip!”Change Flip!”
4 3 3 2 4 3
2 2 4
15 3 5 159. 10.
6 2 4 6
y y a b c a b
a b ac
1. Change Division to Multiplication
2. Flip the 2nd Fraction
3. Simplify (See previous slide)
Multiply or Divide Rational Multiply or Divide Rational FunctionsFunctions
22 3 2 7 2111. 12.
3 2 10 5 2 5 2
x x x
x x x x